'The total return on a portfolio of investments takes into account not only the capital appreciation on the portfolio, but also the income received on the portfolio. The income typically consists of interest, dividends, and securities lending fees. This contrasts with the price return, which takes into account only the capital gain on an investment.'

Which means for our asset as example:- The total return, or increase in value over 5 years of ProShares UltraPro QQQ is 257.9%, which is higher, thus better compared to the benchmark SPY (81.9%) in the same period.
- Compared with SPY (46.1%) in the period of the last 3 years, the total return, or increase in value of 102% is larger, thus better.

'The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (12.7%) in the period of the last 5 years, the annual return (CAGR) of 29.1% of ProShares UltraPro QQQ is greater, thus better.
- Looking at annual return (CAGR) in of 26.4% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (13.5%).

'Volatility is a rate at which the price of a security increases or decreases for a given set of returns. Volatility is measured by calculating the standard deviation of the annualized returns over a given period of time. It shows the range to which the price of a security may increase or decrease. Volatility measures the risk of a security. It is used in option pricing formula to gauge the fluctuations in the returns of the underlying assets. Volatility indicates the pricing behavior of the security and helps estimate the fluctuations that may happen in a short period of time.'

Using this definition on our asset we see for example:- The historical 30 days volatility over 5 years of ProShares UltraPro QQQ is 71%, which is higher, thus worse compared to the benchmark SPY (19.8%) in the same period.
- Compared with SPY (23%) in the period of the last 3 years, the historical 30 days volatility of 79.4% is higher, thus worse.

'Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the upside and downside risk. Specifically, downside risk in our definition is the semi-deviation, that is the standard deviation of all negative returns.'

Which means for our asset as example:- Looking at the downside volatility of 51.5% in the last 5 years of ProShares UltraPro QQQ, we see it is relatively greater, thus worse in comparison to the benchmark SPY (14.5%)
- During the last 3 years, the downside risk is 57.6%, which is higher, thus worse than the value of 16.8% from the benchmark.

'The Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance of an investment by adjusting for its risk. The ratio measures the excess return (or risk premium) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk, named after William F. Sharpe.'

Which means for our asset as example:- Compared with the benchmark SPY (0.52) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.37 of ProShares UltraPro QQQ is lower, thus worse.
- Compared with SPY (0.48) in the period of the last 3 years, the Sharpe Ratio of 0.3 is lower, thus worse.

'The Sortino ratio, a variation of the Sharpe ratio only factors in the downside, or negative volatility, rather than the total volatility used in calculating the Sharpe ratio. The theory behind the Sortino variation is that upside volatility is a plus for the investment, and it, therefore, should not be included in the risk calculation. Therefore, the Sortino ratio takes upside volatility out of the equation and uses only the downside standard deviation in its calculation instead of the total standard deviation that is used in calculating the Sharpe ratio.'

Using this definition on our asset we see for example:- The excess return divided by the downside deviation over 5 years of ProShares UltraPro QQQ is 0.52, which is lower, thus worse compared to the benchmark SPY (0.7) in the same period.
- Looking at ratio of annual return and downside deviation in of 0.41 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.65).

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Applying this definition to our asset in some examples:- Looking at the Ulcer Index of 22 in the last 5 years of ProShares UltraPro QQQ, we see it is relatively higher, thus worse in comparison to the benchmark SPY (6.08 )
- Looking at Ulcer Index in of 23 in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (6.77 ).

'Maximum drawdown is defined as the peak-to-trough decline of an investment during a specific period. It is usually quoted as a percentage of the peak value. The maximum drawdown can be calculated based on absolute returns, in order to identify strategies that suffer less during market downturns, such as low-volatility strategies. However, the maximum drawdown can also be calculated based on returns relative to a benchmark index, for identifying strategies that show steady outperformance over time.'

Which means for our asset as example:- The maximum DrawDown over 5 years of ProShares UltraPro QQQ is -69.9 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum reduction from previous high of -69.9 days is smaller, thus worse.

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Max Drawdown Duration is the worst (the maximum/longest) amount of time an investment has seen between peaks (equity highs) in days.'

Which means for our asset as example:- Compared with the benchmark SPY (139 days) in the period of the last 5 years, the maximum time in days below previous high water mark of 296 days of ProShares UltraPro QQQ is greater, thus worse.
- Looking at maximum time in days below previous high water mark in of 121 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (119 days).

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Avg Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum duration it does not measure only one drawdown event but calculates the average of all.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (35 days) in the period of the last 5 years, the average days under water of 60 days of ProShares UltraPro QQQ is greater, thus worse.
- During the last 3 years, the average days below previous high is 32 days, which is larger, thus worse than the value of 27 days from the benchmark.

Historical returns have been extended using synthetic data.
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- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of ProShares UltraPro QQQ are hypothetical, do not account for slippage, fees or taxes, and are based on backtesting, which has many inherent limitations, some of which are described in our Terms of Use.